The main objective of this grant application is to develop and evaluate improved statistical methods for the design and analysis of epidemiologic studies conducted with outcome-dependent sampling (ODS) schemes under random effects models and nonlinear covariates effects. Extension of the simple ODS design to further improve the study by allowing the sampling probability to depend on the outcome and auxiliary covariates will be developed. Sampling strategies that lead to a more cost-effective design in a given setting will be investigated. The proposed methods are particularly useful for cancer and environmental research because auxiliary information and expensive exposure assessment are frequent challenges. The proposal consists of four projects: The first project deals with linear mixed model regression analysis for an ODS design with a continuous outcome. Two new methods for making inferences about regression parameters in random effects models will be studied: a semi-parametric empirical likelihood approach for observed ODS sample, and a pseudo-likelihood approach for further improving efficiency when the values of the outcome variable are known for the underlying cohort. The second project concerns an efficient ODS design where the sampling probability depends on a continuous outcome and auxiliary covariates. Again, two new methods dealing with different available data structure are proposed. The third project deals with generalized linear mixed effects model analysis for an ODS that depends on both outcome and auxiliary covariates. The last project investigates new statistical methods for nonparametric modeling of nonlinear covariates effects in the logistic regression model under ODS designs. Two methods are proposed: a nonparametric local empirical likelihood method for inference about nonlinear covariates effects when data is collected via ODS designs and a local empirical likelihood method for more general settings where the ODS design depends on outcome and discrete auxiliary covariates. Another method for dealing with continuous auxiliary covariates is also considered. The strengths and weaknesses of each proposed method will be critically examined via theoretical investigations and simulation studies. Comparisons with existing methods will be conducted. Related software will be developed. Data sets from ongoing epidemiologic studies of the effects of environmental exposures, and on cancer and other diseases will be analyzed. [unreadable] [unreadable]